BERLIN, March 27 (Reuters) - German publishing house Bertelsmann reported on Tuesday its slowest growth in annual core profit in three years as earnings decreased at its Arvato business services division.

Core profit at Arvato dropped by 10 percent in 2017, hurt by a decline in earnings at its customer relationship management (CRM) unit, which was put up for sale in January.

Arvato CRM provides services such as live chat, video identification procedures and content moderation for Facebook . It expects to benefit from new business as Facebook steps up efforts to remove fake news and hate speech from its platform, but the business requires heavy investment to keep pace with advances in technology.

Bertelsmann said Arvato CRM - whose competitors include U.S.-based Convergys and TTEC and France's Teleperformance and Webhelp - was hit last year by a slump in business with telecommunications clients and high start-up costs for new clients.

"We are convinced about the growth potential of these activities," Chief Executive Thomas Rabe said on Tuesday, but added that the group wanted to focus on its other businesses.

He was speaking after Bertelsmann, which also owns broadcaster RTL and publishers Gruner + Jahr and Random House, reported that group operating earnings before interest, tax, depreciation and amortisation (EBITDA) edged up 2.7 percent in 2017 to a record high of 2.64 billion euros ($3.3 billion).

Rabe said that the choice of a buyer for Arvato CRM would take into account Bertelsmann's responsibility for the unit's 48,000 employees, without being more specific.

Arvato CRM accounts for around a quarter of Arvato's annual sales of 3.8 billion euros but for "significantly less" than a quarter of the business's earnings, Rabe said.